Spatial and temporal brain transcriptomics has recently emerged as an invaluable data source for molecular neuroscience. The complexity of such data poses considerable challenges for analysis and visualization. We present BrainScope: A web portal for fast, interactive visual exploration of the Allen Atlases of the adult and developing human brain transcriptome. Through a novel methodology to explore high-dimensional data (dual t-SNE), BrainScope enables the linked, all-in-one visualization of genes and samples across the whole brain and genome, and across developmental stages. We show that densities in t-SNE scatter plots of the spatial samples coincide with anatomical regions, and that densities in t-SNE scatter plots of the genes represent gene co-expression modules that are significantly enriched for biological functions. We also show that the topography of the gene t-SNE maps reflect brain region-specific gene functions, enabling hypothesis and data driven research. We demonstrate the discovery potential of BrainScope through three examples: (i) analysis of cell type specific gene sets, (ii) analysis of a set of stable gene co-expression modules across the adult human donors and (iii) analysis of the evolution of co-expression of oligodendrocyte specific genes over developmental stages. Brain- Scope is publicly accessible at www.brainscope.nl.